Nonlinear phenomena have given rise to several outstanding branches of research in phy-sics. Theories and phenomena of nonlinear oscillation, dynamics of competing biological species, hydrodynamics, water waves and waves in nonlinear lattices are explained in some detail. It seems that nonlinearity in many cases causes accumulation of energy as in the case of solitons in nonlinear waves, and stabilization leading to final state as in the case of limit cycle in nonlinear oscillation.
The recent developments of theoretical as well as experimental investigations are reviewed on nonlinear non-steady viscoelastic properties of the polymer systems. The definition of the strain tensor is studied, and some causes of nonlinearity in elastic properties are discussed. Introducing the memory or response function depending on the rate of deformation or relative deformation between “excitation” time and current time, the constitutive equation is extended into nonlinear viscoelastic cases. It is shown that a rate-of-strain dependent model seems to be able to explain some nonlinear non-steady viscoelastic properties such as steady and oscillatory normal stress effect (Weissenberg effect), stress overshoot at the beginning of a flow, stress relaxation after stoppage of flow, some phenomena in the superposition experiments of an oscillatory shear deformation onto a steady flow and so on.
A study of gas breakdown induced by the ultraviolet second harmonic of a single mode ruby laser has revealed an anomalously high threshold intensity for hydrogen. In addition, it has been demonstrated for the first time that the focal volume dependence of the breakdown threshold of a number of molecular and noble gases is influenced by the wavelength of the incident radiation. Evidence for the self-focusing in the ultraviolet gas breakdown has been obtained by measuring the spectral characteristics of the forward scattered radiation.
Carbon fibers having 25 cm in length have been grown successfully, at a relatively low temperature range of about 1000°C, by means of thermal decomposition of vaporized hydrocarbon such as benzene. The structure, effect of heat treatment and growth process were investigated. These fibers had a turbostratic stacking arrangement of the carbon-hexagon networks, whose apparent crystallite sizes La and Lc were about 30_??_40Å, and had a high degree of preferred orientation where the c-axes of the graphite-like layers were nearly perpendicular to the fiber axis with an orientation parameter Ψ1/2=15°. From electron microscopic observations, they were found to consist of concentric layers similar to the annual rings of a tree. By heat treatment at high temperatures, the crystallinity and orientation parameter of the fibers were markedly improved. The growth process of the carbon fibers could be divided into three stages; nucleation, elongation and thickening processes.
An experiment on ultrasonic holography using an array of receivers in a line was conduc-ted. Comparing with the method by scanning a single receiver, some problems in the array method are discussed. Its advantage as an electronic reference wave to the effect of directivity of the transmitter and the receiver is pointed out. Moving the one dimensional array mechani-cally, ultrasonic holograms are constructed by the coherent background method and electronic reference method. Reconstructed images by these methods are shown and compared. These experiments suggest the possibility of a progress to a new holographic technique in which the fixed one dimensional array of receivers is combined with a moving source or object.
Theoretical analysis is given on coherent two-photon propagation resulting in self-induced transparency for three-level systems by means of coupling the Schrodinger and Maxwell equa-tions. The resulting equations newly yield a two-photon area theorem by defining an area integration of the product of two fields Κ_??_ ελευdt, where ελ, and ευ are the optical field intensities with different frequencies and Κ is a constant characterizing the two-photon transi-tion. The derived two-photon area equations with numerical analysis predict a coherent pro-pagation with novel modulation, transmission and pulse advance or delay in pulse formation. These predictions are compared with measurements. The observed low loss propagation and pulse breakup with peak amplification, pulse advance and delay for the three-level system in potassium vapor are referred to as resulting from the two-photon self-induced transparency due to coherent interaction.
The present parper discusses the initiation and growth of trees in polystrene and polyvinyl chrolide for the range of temperature from 20°C to 80°C. The relation between the applied voltage (V) and the time (t) for tree initiation at 50% of full growth is given by log t=Const-nlogV (1) At each temperature there is a critical applied voltage (Vc) beyond which the value of n begins to decrease. From the values of n obtained by eq. (1) it is considered that above Vc, where the voltage dependence is large, the trees initiate by electrothermal breakdown. On the other hand, below Vc, where the voltage dependence is small, the trees appear to initiate by electromechanical breakdown. For polymeric dielectric materials (for example, silicone rubber) whose Young's modulus is below 108 dyn/cm2, a void is formed between the needle tip and polymer. The void is thought to be formed by Maxwell stress.